x^4-14x^2+15=0

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Solution for x^4-14x^2+15=0 equation:


Simplifying
x4 + -14x2 + 15 = 0

Reorder the terms:
15 + -14x2 + x4 = 0

Solving
15 + -14x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -14x2 + -15 + x4 = 0 + -15

Reorder the terms:
15 + -15 + -14x2 + x4 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -14x2 + x4 = 0 + -15
-14x2 + x4 = 0 + -15

Combine like terms: 0 + -15 = -15
-14x2 + x4 = -15

The x term is -14x2.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x2 + 49 + x4 = -15 + 49

Reorder the terms:
49 + -14x2 + x4 = -15 + 49

Combine like terms: -15 + 49 = 34
49 + -14x2 + x4 = 34

Factor a perfect square on the left side:
(x2 + -7)(x2 + -7) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(x2 + -7) equal to 5.830951895 and -5.830951895.

Subproblem 1

x2 + -7 = 5.830951895 Simplifying x2 + -7 = 5.830951895 Reorder the terms: -7 + x2 = 5.830951895 Solving -7 + x2 = 5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = 5.830951895 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = 5.830951895 + 7 x2 = 5.830951895 + 7 Combine like terms: 5.830951895 + 7 = 12.830951895 x2 = 12.830951895 Simplifying x2 = 12.830951895 Take the square root of each side: x = {-3.582031811, 3.582031811}

Subproblem 2

x2 + -7 = -5.830951895 Simplifying x2 + -7 = -5.830951895 Reorder the terms: -7 + x2 = -5.830951895 Solving -7 + x2 = -5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = -5.830951895 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = -5.830951895 + 7 x2 = -5.830951895 + 7 Combine like terms: -5.830951895 + 7 = 1.169048105 x2 = 1.169048105 Simplifying x2 = 1.169048105 Take the square root of each side: x = {-1.081225279, 1.081225279}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.582031811, 3.582031811, -1.081225279, 1.081225279}

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